Euler Obstruction and Defects of Functions on Singular Varieties

Several authors have proved Lefschetz type formulae for the local Euler obstruction. In particular, a result of this type is proved in [BLS].The formula proved in that paper turns out to be equivalent to saying that the local Euler obstruction, as a constructible function, satisfies the local Euler condition (in bivariant theory) with respect to general linear forms. The purpose of this work is to understand what prevents the local Euler obstruction of satisfying the local Euler condition with respect to functions which are singular at the considered point. This is measured by an invariant (or ``defect'') of such functions that we define below. We give an interpretation of this defect in terms of vanishing cycles, which allows us to calculate it algebraically. When the function has an isolated singularity, our invariant can be defined geometrically, via obstruction theory. We notice that this invariant unifies the usual concepts of {\it the Milnor number} of a function and of the {\it local Euler obstruction} of an analytic set.Comment: 18 page

Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction

We compute how bulk loops renormalize both bulk and brane effective interactions for codimension-two branes in 6D gauged chiral supergravity, as functions of the brane tension and brane-localized flux. We do so by explicitly integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing the results of a companion paper, arXiv:1210.3753, to the supersymmetric case. While the brane back-reaction generically breaks supersymmetry, we show that the bulk supersymmetry can be preserved if the amount of brane-localized flux is related in a specific BPS-like way to the brane tension, and verify that the loop corrections to the brane curvature vanish in this special case. In these systems it is the brane-bulk couplings that fix the size of the extra dimensions, and we show that in some circumstances the bulk geometry dynamically adjusts to ensure the supersymmetric BPS-like condition is automatically satisfied. We investigate the robustness of this residual supersymmetry to loops of non-supersymmetric matter on the branes, and show that supersymmetry-breaking effects can enter only through effective brane-bulk interactions involving at least two derivatives. We comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.Comment: 49 pages + appendices. This is the final version to appear in JHE

Order and Disorder in AKLT Antiferromagnets in Three Dimensions

The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O(3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Neel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure

Low Temperature metamagnetism and Hall effect anomaly in Kondo compound CeAgBi2

Heavy fermion (HF) materials exhibit a rich array of phenomena due to the strong Kondo coupling between their localized moments and itinerant electrons. A central question in their study is to understand the interplay between magnetic order and charge transport, and its role in stabilizing new quantum phases of matter. Particularly promising in this regard is a family of tetragonal intermetallic compounds Ce{$TX$}$_2$ ($T=$ transition metal, $X=$ pnictogen), that includes a variety of HF compounds showing $T$-linear electronic specific heat $\bf{C_e \sim \gamma T}$, with $\gamma\sim$ 20-500 mJ$\cdot$mol$^{-1}$~K$^{-2}$, reflecting an effective mass enhancement ranging from small to modest. Here, we study the low-temperature field-tuned phase diagram of high-quality CeAgBi$_2$ using magnetometry and transport measurements. We find an antiferromagnetic transition at ${T_{N} = 6.4}$~K with weak magnetic anisotropy and the easy axis along the $c$-axis, similar to previous reports (${T_{N} = 6.1}$~K). This scenario, along with the presence of two anisotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, leads to a rich field-tuned magnetic phase diagram, consisting of five metamagnetic transitions of both first and second order. In addition, we unveil an anomalous Hall contribution for fields $H<54$ kOe which is drastically altered when $H$ is tuned through a trio of transitions at 57, 78, and 84~kOe, suggesting that the Fermi surface is reconstructed in a subset of the metamagnetic transitions.Comment: (*equal contribution

Testing general relativity using golden black-hole binaries

The coalescences of stellar-mass black-hole binaries through their inspiral, merger, and ringdown are among the most promising sources for ground-based gravitational-wave (GW) detectors. If a GW signal is observed with sufficient signal-to-noise ratio, the masses and spins of the black holes can be estimated from just the inspiral part of the signal. Using these estimates of the initial parameters of the binary, the mass and spin of the final black hole can be uniquely predicted making use of general-relativistic numerical simulations. In addition, the mass and spin of the final black hole can be independently estimated from the merger--ringdown part of the signal. If the binary black hole dynamics is correctly described by general relativity (GR), these independent estimates have to be consistent with each other. We present a Bayesian implementation of such a test of general relativity, which allows us to combine the constraints from multiple observations. Using kludge modified GR waveforms, we demonstrate that this test can detect sufficiently large deviations from GR, and outline the expected constraints from upcoming GW observations using the second-generation of ground-based GW detectors.Comment: 5 pages, 2 fig

Observation of Coherent Helimagnons and Gilbert damping in an Itinerant Magnet

We study the magnetic excitations of itinerant helimagnets by applying time-resolved optical spectroscopy to Fe0.8Co0.2Si. Optically excited oscillations of the magnetization in the helical state are found to disperse to lower frequency as the applied magnetic field is increased; the fingerprint of collective modes unique to helimagnets, known as helimagnons. The use of time-resolved spectroscopy allows us to address the fundamental magnetic relaxation processes by directly measuring the Gilbert damping, revealing the versatility of spin dynamics in chiral magnets. (*These authors contributed equally to this work

Pulmonary tuberculosis in outpatients in Sabah, Malaysia: Advanced disease but low incidence of HIV co-infection

BackgroundTuberculosis (TB) is generally well controlled in Malaysia, but remains an important problem in the nation&rsquo;s eastern states. In order to better understand factors contributing to high TB rates in the eastern state of Sabah, our aims were to describe characteristics of patients with TB at a large outpatient clinic, and determine the prevalence of HIV co-infection. Additionally, we sought to test sensitivity and specificity of the locally-available point-of-care HIV test kits.MethodsWe enrolled consenting adults with smear-positive pulmonary TB for a 2-year period at Luyang Clinic, Kota Kinabalu, Malaysia. Participants were questioned about ethnicity, smoking, prior TB, disease duration, symptoms and comorbidities. Chest radiographs were scored using a previously devised tool. HIV was tested after counselling using 2 point-of-care tests for each patient: the test routinely in use at the TB clinic (either Advanced Quality&trade; Rapid Anti-HIV 1&amp;2, FACTS anti-HIV 1/2 RAPID or HIV (1 + 2) Antibody Colloidal Gold), and a comparator test (Abbott Determine&trade; HIV-1/2, Inverness Medical). Positive tests were confirmed by enzyme immunoassay (EIA), particle agglutination and line immunoassay.Results176 participants were enrolled; 59 (33.5%) were non-Malaysians and 104 (59.1%) were male. Smoking rates were high (81/104 males, 77.9%), most had cavitary disease (51/145, 64.8%), and 81/176 (46.0%) had haemoptysis. The median period of symptoms prior to treatment onset was 8 weeks. Diabetes was present in 12. People with diabetes or other comorbidities had less severe TB, suggesting different healthcare seeking behaviours in this group. All participants consented to HIV testing: three (1.7%) were positive according to Determine&trade; and EIA, but one of these tested negative on the point-of-care test available at the clinic (Advanced Quality&trade; Rapid Anti-HIV 1&amp;2). The low number of positive tests and changes in locally-available test type meant that accurate estimates of sensitivity and specificity were not possible.ConclusionPatients had advanced disease at diagnosis, long diagnostic delays, low HIV co-infection rates, high smoking rates among males, and migrants may be over-represented. These findings provide important insights to guide local TB control efforts. Caution is required in using some point-of-care HIV tests, and ongoing quality control measures are of major importance